Centre Inria d'Université Côte d'Azur

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20052025

most citedA Neural-Network-Based Model Predictive Control of Three-Phase Inverter With an Output LC Filter

231 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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16 papers · 1 filter

math.AG2020

Patchworking real algebraic hypersurfaces with asymptotically large Betti numbers

Charles Arnal

In this article, we describe a recursive method for constructing a family of real projective algebraic hypersurfaces in ambient dimension $n$ from families of such hypersurfaces in…

math.AG2020

Determinantal tensor product surfaces and the method of moving quadrics

Laurent Busé, Falai Chen

A tensor product surface $S$ is an algebraic surface that is defined as the closure of the image of a rational map $ϕ$ from $P^{1} \times P^{1}$ to $\mathbb{…

math.AG2018★ 8 cited

Skew-Symmetric Tensor Decomposition

Enrique Arrondo, Alessandra Bernardi, Pedro Macias Marques +1

We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in { $⋀^{d} V_{C}$ with $d\leq…

math.AG2018★ 12 cited

Degree and birationality of multi-graded rational maps

Laurent Busé, Yairon Cid-Ruiz, Carlos D'Andrea

We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their alge…

math.AG2018★ 1 cited

Freeness and invariants of rational plane curves

Laurent Busé, Alexandru Dimca, Gabriel Sticlaru

Given a parameterization $ϕ$ of a rational plane curve C, we study some invariants of C via $ϕ$ . We first focus on the characterization of rational cuspidal curves, in particular w…

math.AG2015★ 9 cited

Waring-like decompositions of polynomials - 1

Maria Virginia Catalisano, Luca Chiantini, Anthony V. Geramita +1

Let $F$ be a homogeneous form of degree $d$ in $n$ variables. A Waring decomposition of $F$ is a way to express $F$ as a sum of $d^{t h}$ powers of linear forms. In this paper we co…

math.AG2015★ 23 cited

Certifying isolated singular points and their multiplicity structure

Jonathan D. Hauenstein, Bernard Mourrain, Agnes Szanto

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion…

math.AG2014★ 1 cited

Border Basis relaxation for polynomial optimization

Marta Abril Bucero, Bernard Mourrain

A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic clos…

math.AG2014

Bounds on the dimension of trivariate spline spaces: A homological approach

Bernard Mourrain, Nelly Villamizar

We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lo…

math.AG2013★ 7 cited

Exact relaxation for polynomial optimization on semi-algebraic sets

Marta Abril Bucero, Bernard Mourrain

In this paper, we study the problem of computing by relaxation hierarchies the infimum of a real polynomial function f on a closed basic semialgebraic set and the points where this…

math.AG2012★ 29 cited

Homological techniques for the analysis of the dimension of triangular spline spaces

Bernard Mourrain, Nelly Villamizar

The spline space $C_{k}^{r} (Δ)$ attached to a subdivided domain $Δ$ of $R^{d}$ is the vector space of functions of class $C^{r}$ which are polynomials of degree $\leq k$ on each piece…

math.AG2012★ 2 cited

Curvilinear schemes and maximum rank of forms

Edoardo Ballico, Alessandra Bernardi

We define the \emph{curvilinear rank} of a degree $d$ form $P$ in $n + 1$ variables as the minimum length of a curvilinear scheme, contained in the $d$ -th Veronese embedding of $\mat…

math.AG2011

Moment Matrices, Border Bases and Real Radical Computation

Jean-Bernard Lasserre, Monique Laurent, Bernard Mourrain +2

In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches…

math.AG2011★ 49 cited

General Tensor Decomposition, Moment Matrices and Applications

Alessandra Bernardi, Jerome Brachat, Pierre Comon +1

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous t…

math.AG2010★ 48 cited

Decomposition of homogeneous polynomials with low rank

Edoardo Ballico, Alessandra Bernardi

Let $F$ be a homogeneous polynomial of degree $d$ in $m + 1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$ -th se…

math.AG2009

Modular Las Vegas Algorithms for Polynomial Absolute Factorization

Cristina Bertone, Guillaume Chèze, André Galligo

Let $f(X,Y) \in \ZZ[X,Y]$ be an irreducible polynomial over $\QQ$. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of $f$ , or more preci…